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We all have to look things up once in a while, and I can tell you right now that Wikipedia is the best source for practical information on mathematics. But, there are some others out there that are also worth knowing. Most of these sites are encyclopedic, and not meant for browsing top down, so I’ve used the entry for eigenvector as an example for… read more

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I was going to call this article War on Spam. But, given how well my experiments went, I had to retitle it Skirmish with Spam. Lately, the number of spam attempts has risen so much that even Mollom lets through enough spam to get me a bit miffed. So, I decided to go “old school”… I was going to add math problems of increasing difficulty until… read more

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The first three articles on tomography focused on analytic techniques, in which the reconstruction problem is attacked using mathematical analysis. When the step to real world scanners is made, the problem is discretized. Both the projections and the reconstruction area are divided into pixels, and a numerical approximation of the true mathematical technique is introduced. The algebraic techniques assume… read more

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At the end of the second article on tomography, I left you with a very blurry reconstruction of the scanned object. Indeed, naive backprojection is not sufficient to create high-quality reconstructions. Why is that so? Intuitively, a simple backprojection cannot be expected to create a perfect reconstruction, since the contribution of… read more

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This article shows that it is possible to reconstruct the inside of a person or object from (lots of) projections of that person or object. Mathematically, tomography is based on the fact that the function values of a two-dimension functional \(f(x,y)\) can be calculated from projections of that function. This basic fact was discovered… read more

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Have you ever wondered how a CT (or CAT) scanner creates an image of the inside of a person? The answer is computing. CT and CAT are short for computed (axial) tomography. Computing is the secret sauce that is poured over the hundreds or thousands of X-ray photos that make up a CT scan, to merge them into a single image. This first article on tomography explains projections, the essential input data for tomography… read more

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In the article Color QR Codes Done Right, I’ve tried to convince you to create your color QR codes in a way that keeps them easily scannable. This week, I’ve discovered Visualead, a startup that is currently in Public Beta, that lets you combine any artwork with a QR code. Graphically, they have nailed it. They seem to have found out that… read more

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To the guys that stole my car: I feel that your action was suboptimal with respect to building a better society. Also, breaking open a locker while a guy is in the swimming pool is not generally considered a nice thing to do. I do agree with your point of view that… read more

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Quite a while ago, I briefly reported on the spectacular Mars Science Laboratory mission that is currently under way. As you are probably aware, the Curiosity rover has now safely landed, and is already exploring the Red Planet. In this article, I want to tell you about the spectacular way in which the rover was put down on the surface. For previous Mars rovers like… read more